We consider the nonlinear eigenvalue problem
where are constants and is a parameter. It is known in  that the bifurcation curve consists of two branches, which are denoted by . Here, . We establish the asymptotic behavior of the turning point of , namely, the point which satisfies as and . We also establish the asymptotic formulas for and as and , respectively.
Submitted June 20, 2016. Published July 27, 2016.
Math Subject Classifications: 34F10.
Key Words: Asymptotic behavior; parabola-like bifurcation curves.
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| Tetsutaro Shibata |
Laboratory of Mathematics
Institute of Engineering
Higashi-Hiroshima, 739-8527, Japan
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